Alternant hydrocarbons mirror image theorem

From this mirror-image theorem it follows that MCD spectra of uncharged alternant systems that are paired with themselves should be zero. This is only true within the confines of the above approximations, in which the y." contributions to the MCD are neglected. The y contributions are in fact zero for uncharged alternant hydrocarbons since from the pairing theorem it follows that AHOMO = ALUMO. 

Charged alternant hydrocarbons occur as pairs of negatively and positively charged ions, and the pairing theorem relates the states of the former to the states of the latter. While at the standard PPP level of theory the absorption spectra of the members of a pair are predicted to be identical, and indeed experimentally almost exactly are, their MCD spectra are expected to be mirror images of each other and indeed nearly are (e.g., diphenylmethyl anion and cation). ... 

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